A challenge given to Ben Heck in March of last year was "Challenge - cheap 3D printer" (design a 3D printer more cheaply), and that thread continues to receive replies to this date. Unfortunately nobody in that thread actually addressed the matter as a design issue. Instead, most of the replies (including from Ben) seem to have addressed an entirely different question, how to build the same kind of 3D printer as you can buy today, but for less money.
Those are two completely different questions. It was pointed out by Ben that because of the race to the bottom by a huge number of manufacturers, the current designs can't be made a lot cheaper while still retaining the same speed and accuracy. That's probably correct with respect to current standard designs, but it says nothing at all about different designs.
So, this thread suggests a different design approach that may offer a solution, and it's a pretty natural step to take.
A useful observation with which to start is that the accuracy and precision obtainable with today's RepRap-style models stems from the design of their stepper motors and the limitations inherent in screw drives and belts and pulleys and the rigidity of their physical construction. Because of this, if you retain the existing design model but in the quest for lower cost you compromise on one of these areas, you are very likely to lose the necessary degree of printing accuracy even if you are performing steps at very high resolution, so that's not likely to be a good way forward. Printing with high precision in the wrong place is not helpful.
That observation about accuracy and precision leads us directly to a solution though. Engineers know full well how to gain high and definable accuracy without each of the components being manufactured to extreme tolerances, and that's by using closed-loop control with negative feedback, the basis of servo-systems. In a closed-loop system, the only thing that needs to be highly accurate and with known precision is determination of current position, and the heart of that need be nothing more costly than a very accurately printed graticule which can be produced for pennies. Given the ability to know where the operating head is located very accurately in each relevant axis (not necessarily Cartesian), the only other requirement for maintaining that limit of accuracy is rigidity of coupling between sensors and operating head, ie. the hot end in a 3D printer. Very importantly, there is no need for rigidity in the motor assemblies --- as long as they're moving the head in the right direction, that's good enough.
So, I'll recast the original question differently and tie it to this specific way forward:
"How can we design a 3D printer based on closed-loop control to gain high accuracy and overcome low cost construction through use of negative feedback?"
It's mostly a matter of examining alternative physical arrangements to find one with good rigidity while also having low suspended mass and being amenable to construction with today's open-loop 3D printers as a stepping stone. It's worth pointing out that virtually all 2D inkjet printers already use closed-loop control --- if you take one apart you'll find a positional sensor and fine graticule in there somewhere to provide very high accuracy in one dimension at the lowest cost.
Once we start thinking about closed-loop control for 3D printers, many possible advantages start to appear:
- As already mentioned, it compensates for low-quality parts, so prices could fall much lower.
- Closed loop operation compensates for latitude at assembly time as well, also leading to lower costs.
- Very much higher accuracy than we have today is possible, and that cannot be done open loop.
- Motors of many different kinds can be used, AC, DC, brushed, brushless, linear, and also steppers.
- If steppers are used in a closed-loop system, you can overdrive them without worrying about "lost steps" because the steps aren't used for position control anyway, yet you still retain the advantage of high holding torque.
- Much higher speeds are possible than we have today because of the two-fold advantage of wider motor choice and arbitrarily high acceleration while the control loop seeks to its desired position.
- Accuracy and precision are more independently controllable in closed-loop systems. This provides more opportunities for cost reduction through tradeoffs, as well as dynamic optimization in favour of speed, for example on in-fill. In open-loop printers with stepper motors, the step size places a limit on precision of positional control, but this is very rarely reflected in the accuracy of actual positioning which is primarily determined by physical construction.
I'm sure there are many other benefits.
The main disadvantage is that this direction requires new thinking, new solutions. And there's the challenge! 
Morgaine.
